- #1
Thorn
- 23
- 0
The question:
If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive prime P?
Where G(n)={a e G| |a| = n^(k) for some k is greater than or equal to 0}...That is the set of all a in G, s.t. the order of a is some power of n. (But since it is the additive group, I suppose it would just a be a multiple of n)
How do I even begin with this? Aren't the elements of Q/Z sets? The collections of right cosets? and don't they have infinite order?...
If G is the additive group Q/Z, what are the elements of the subgroup G(2)? Of G(P) for any positive prime P?
Where G(n)={a e G| |a| = n^(k) for some k is greater than or equal to 0}...That is the set of all a in G, s.t. the order of a is some power of n. (But since it is the additive group, I suppose it would just a be a multiple of n)
How do I even begin with this? Aren't the elements of Q/Z sets? The collections of right cosets? and don't they have infinite order?...